Help find 2 quadratic function problems in junior high school math

1. Solution: Let the function expression of this parabola be y ax bx c(a≠) and substitute the coordinates of a, b, and c into the three points.

a＋b＋c＝－40

7²a＋7b＋c＝8

5）²a＋（－5）b＋c＝20

From the above three simultaneous solutions, the expression of the parabola is y

2. Solution: Let the function expression of this parabola be y a(x m) k(a≠0) because of the vertex coordinates (3,3), so m 3, k 3 so y=a(x-3) +3

Substituting the above equation from the point (1,1) of this function yields a (1 3) 3 solution

Therefore, the functional expression of this parabola is y

The second one can be set to the vertex formula, y=a(x 3) 3, and then (1,1) with x, y is calculated as a, and the first one can be set to y=ax +bx+c, and the three point coordinates are brought into the ...... of solving the system of equations

1) Let the parabolic equation be y=ax 2+bx+c, and substitute a, b, and c into the system of equations to solve the equation, and the values of a, b, and c (x 2 is the square of x, the same below).

2) Let the parabolic equation be y=(x-h) 2+k, and substitute two points into the system of equations to solve the equation to find the value of h,k.

I won't do the answer, the process is for you

y=ax +bx+c brings three points into solving the ternary equation and we get a= b=-4 c=

y=a[x-m] +k [ y=a[x-3] +3 [ y=a[-2]+3 a=

y= +3

The axis of symmetry is parallel to the y-axis, y=ax 2+bx+c, and a, b, and c can be obtained by substituting a, b, and c into the three points.

The axis of symmetry is parallel to the y-axis, y=ax 2+bx+c, and substituting (3,3), (1,1), and (5,1) into the three points yields a, b, and c.

The axis of symmetry is parallel to the x-axis, x=ay 2+by+c, and substituting (3,3), (1,1), and (1,5) into a, b, and c can be obtained.

This question is correct.

The set price is x and the profit is y

Rule. The equation is:

y=x(x-60)

If you don't understand, you can ask.

Solution: If the 20 cm wire is cut into x cm and the sail is 20-x cm, then the area of the square enclosed by these two sections of wire is (x 4) 2, [(20-x) 4] 2, so the sum of the areas of these two squares y,y (x 4) 2 + [(20-x) 4] 2

1／16（2x^2-40x＋400）

1 Hail 8 (x 2-20x 200).

1／8（x^2-20x＋100＋100）

1／8（x-10）^2＋

When x 10, the minimum value of y hail is fierce in square centimeters.

You're right, and the answer is 25 2

From the known y=2x -4mx+m =2(x-m) -m, so that y=0 obtains: x=m+m*root number 2 2 or x=m-m*root number 2 2

So ab = absolute value (m * root number 2) so the area of abc s = 1 2 * absolute value (m * root number 2) * m = 4 root number 2

The solution yields m=2 or m=-2

m = plus or minus 2

The two intersection points are (1 plus minus 1 2 root number 2) m

The vertex ordinate is -m 2

So there is (plus or minus root number) 2m*m 2 2 = 4 times the root number 2 solution to m is plus or minus 2.

Forgive this disgusting process, but it can only be written in Chinese like this.

The original formula 2(x-m) m, so the coordinates of point c (m, m), xa+xb 2m, xa*xb m 2

So ab distance |xa－xb|(xa+xb) 4xa*xb 2m so area

So m 32 open to the 8th power.

ab=[root(-4m)2-8m2] 2

The ordinate of c = [8m2-(-4m)2] 4

sabc=ab*|yc|= 4 root number 2

Calculate it yourself later.。。

1) Connect AC, because AB is the diameter, so ABC is a right triangle, so, OC = ao*bo, in y=1 6 x 2-mx+n, let x=0, cong dan gets y=n, so c(0,n), oc=-n, let the two roots of the equation be x1, x2, then a(x1,0), b(x2,0), ao=-x1, bo=x2, and by Vedr's theorem, x1+x2=6m, x1*x2=6n, so, n =-6n, get n=- 6。

2) 1 x1+1 x2=(x1+x2) (coarse x1*x2)=m n=5 36, so m=-5 6, and then x1=-9,x2=4, so a(-9,0),b(4,0),c(0,Yanzheng number-6).

3) When PM is parallel to AC, there is PBM similar to ABC, at this time, OPQ is similar to OAC, so OP:OA=OQ:BC, that is, (9-K):9=K:6, the solution is K=.

Hope it helps!

When x=0, y=n, so the coordinates of c are (0,n) and we can get the product of n less than 0=n 2=-6n (according to the nature of the height of the right triangle) to get n = -6, and then according to the two and the ruler to lift the year, answer the empty two root product = 5 36 to get m = c (0, -6).

The AB point can be found from the known mn.

The similarity in the back is very good, you can do it yourself, Lingjiao, I'll go to sleep